Navigation system



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Jnven/or: HLex-omev 'Pricbodjko 1B 6pwwn x; ficu z United States Patent3,316,550 NAVIGATION SYSTEM Alexander Prichodjko, Oberelchingen, KreisNeu-Ulm, Germany, assignor to Telefunken Patentverwertungs G.m.b.H., Ulm(Danube), Germany Filed July 8, 1963, Ser. No. 293,472 Claims priority,application Germany, July 6, 1962, T 22,421, T 22,422, T 22,423 36Claims. (Cl. 34315) The present invention relates to a navigationsystem.

More particularly, the present invention relates to a method andapparatus for determining the distance between the plane in which lies apoint in space and the plane of symmetry between two high frequencystations which serve for navigational purposes and operate on thetransit time principle.

Co-pending application Ser. No. 267,306, filed Mar. 22, 1963, ofAlexander Prichodjko, Albert Simianer, and Hartmut Hipp, and co-pendingapplication Ser. No. 270,909, filed Apr. 5, 1963, of AlexanderPrichodjko, relate to systems for determining the distance x-see FIG-URE 1 of the accompanying dr-awin.gsbetween a positional plane Fcontaining a point P and the plane of symmetry P of two points E and Espaced apart a known distance g, at each of which points E and E thereis a high frequency station. The distance x is calculated by means of aconventional computer which solves the equation where the distance ebetween E and P and the distance 2 between E and P are determinedaccording to the transit time principle. The algebraic sign of xrepresents the particular side of the plane of symmetry F on which theplane F is located.

Systems of the above type may be used for aerial navigation, in whichcase the points E and E represent fixed ground stations of knownlocation and the point P the unknown position of an aircraft. Asdisclosed in the above-mentioned applications, the system may be soarranged that the distance x is calculated either at or in conjunctionwith one of the ground stations, or at point P, i.e., aboard theaircraft. The calculation, however, involves the formation of sums,differences, products and quotients, and the hardware needed to carryout these tasks is, at least at present, too expensive to permitwidespread use.

It is, therefore, an object of the present invention to provide a methodand apparatus which operates on the above-described basic principle,i.e., a method and apparatus for determining the distance x on the basisof the above equation, which method and apparatus operate as simply aspossible and which require substantially less hardware. With this basicobject in view, the present invention resides, basically, in a methodand apparatus wherein the distance x between a positional plane Fcontaining a point P and the plane of symmetry F between two highfrequency stations at E and E which are spaced apart a distance g isdetermined as follows:

(1) The two expressions (e +e and (e -e appearing in the above Equation1 occur during the measurement operation in form of two transit timesections.

(2) These two transit time sections are transformed into pulse trainscontaining pulses of a pulse repetition frequencyf 3,316,550 PatentedApr. 25, 1967 (3) The two numbers of period durations of the pulserepetition frequency j which, when summed up into pulse trains, occupythe same amount of time as the two transit time sections are determinedby counting. The two counted values are then multiplied by each other,in the strict mathematical sense.

Here, e and e represent the paths or distances between E, and P and Eand P, respectively, along which travel the time marker signals usedbefore the measurement operation to mark the beginnings and the ends ofthe transit time sections T and T 0 represents the propagation velocityof these time marker signals; and D represents an arbitrarily selectableunit of length into which g is to be substituted.

According to one method for counting the pulse sequences within thetransit time sections, the pulse repetition frequency is given in such amanner that the result of the counting operation is numerically equal tothe length, in the desired unit of length, of the transit pat-hcorresponding to the transit time section. In contradistinction thereto,the pulse repetition frequency of the pulse train is, according to thepresent invention, given in such a manner that the product formed of thetwo counted values thereby is numerically equal to the numerical valueof the distance x.

In order to obtain and to derive (2), Equation 1 can be written asfollows:

=p'q whose factors p and q, respectively, represent the sum of thepulses of a pulse repetition frequency f counted for the duration of thetransit time sections T and T wherein 1+ z TFT (5) and Using theexpressions in Equations 5 and 6 in Equation 4, there is obtainedAccording to another feature of the present invention, the equation isintroduced, wherein n is a dimensionless proportionality constant.

Equation 7 thus becomes which can be re-written as 2n (12) 1f Equation12 is substituted in Equation 8, there is then obtained for the pulserepetition frequency f the relationship given in Equation 2, whosevalidity was to be proved.

The factor n in Equation 8 can be freely selected, it being pointed out,however, that when n is high, a large counting accuracy is obtained. Itis expedient, however, additionally to select 11 such that the numericalvalue of D in Equation 12 becomes an integral power of ten, so that xcan easily be obtained from x simply by shifting the decimal point toobtain the order of the digits within the numerical expression of x.

If x is to be obtained other than as a numerical value identical to gwith reference to the dimension D but in a difierent dimension D'zk-Dwhere k is an arbitrarily selectable constant, it is better not tooperate with according to Equation 12, but instead with in which case,however, it is advantageous to select (u-n)=n so that D becomes anintegral power of ten.

It is well established that if the sum and difference are formed fromtwo measured values, the difference will always have a larger percentageerror than the sum. It is therefore not necessary that the transit timesections T and T (cf., Equations 5 and 6) be counted outwith pulseshaving the same pulse repetition frequency 1; instead, the countingoperation can, according to another feature of the instant invention, besimplified by using different pulse repetition frequencies i and i frelating to section T and f to section T Here f is smaller than f andshould be selected on the basis of the following.

If f and i respectively, are substituted for f in Equation 7, there isobtained and from Equations 15 and 16 corresponding Equation 14, forexample, for the frequency f,,, there is obtained The present inventionwill now be described in detail, with reference to the accompanyingdrawings, in which:

FIGURE 1, already referred to above, shows the relative positions of twoknown points and one unknown point.

FIGURE 2 is a block diagram of a system according to the presentinvention.

FIGURE 3 is a block diagram of a modified system according to theinstant invention.

FIGURE 4 shows a pulse train constituting the output of one of the gatecircuits of either of the systems of FIG- URES 2 and 3.

FIGURE 5 is a block diagram of a first basic embodiment of a systemaccording to the present invention.

FIGURE 6 shows the timed relationship of signals appearing at the outputof one of the components of the system of FIGURE 5.

FIGURE 7 is a block diagram of a modification of the system of FIGURE 5.

FIGURE 8 is a block diagram showing the details of an output stageforming part of the system of FIGURE 5.

FIGURE 9 is a block diagram showing the details of the actual outputcircuit incorporated in FIGURE 8.

FIGURE 10 shows the timed relationship of signals as they are producedaccording to a second basic embodiment of the present invention.

FIGURE 11 is a block diagram of the second basic embodiment of a systemaccording to the instant invention.

FIGURE 12 is a block diagram showing the details of an output stageforming part of the system according to FIGURE 11.

FIGURE 13 is a block diagram showing the details of the actual outputcircuit incorporated in FIGURE 12.

FIGURE 14 is a block diagram of a third basic embodiment of a systemaccording to the present invention.

FIGURE 15 shows the timed relationship of signals as they are producedaccording to the third basic embodiment.

FIGURE 16 is a block diagram showing an inversion of the systemaccording to the first basic embodiment of the invention.

FIGURE 17 is a block diagram showing an inversion of the systemaccording to the second basic embodiment of the invention.

FIGURE 18 is a block diagram showing an inversion of the systemaccording to the third basic embodiment of the invention.

FIGURE 19 shows a modification of the output stage of FIGURE 8.

FIGURE 20 shows a modification of the output circuit of FIGURE 9 whenthe same forms part of the modification of FIGURE 19.

FIGURE 21 shows a modification of the output stage of FIGURE 12.

FIGURE 22 shows a modification of the output circuit of FIGURE 13 whenthe same forms part of the modification of FIGURE 21.

FIGURE 23 shows a modification of a portion of the system of FIGURE 14,in which case the output circuit will likewise be modified as shown inFIGURE 22.

Referring now once again to the drawings and to FIG- URES 2 and 3thereof in particular, the same show, in block diagram form, two systemsaccording to the present invention for utilizing the informationcontained in the transit time sections T and T the circuit of FIGURE 2operating with a common pulse repetition frequency f and the circuit ofFIGURE 3 operating with a first pulse repetition frequency f and asecond pulse repetition frequency f The output signals of blocks 1 and 2represent the transit time sections T and T respectively, and consisteach of a pulse for opening the gate circuits 3, 3; 4, 4', the durationof which pulses corresponds to the duration of the transit timeintervals T and T respectively. In FIGURE 2, component 5 is a pulsegenerator producing pulses at the pulse repetition frequency 1, whichpulses are applied to gate circuits 3 and 4, while in FIGURE 3 pulsegenerators 6 and 7 produce pulses at the pulse repetition frequencies fand f respectively, which pulses are applied to gate circuits 3 and 4',respectively.

The output of, for example, gate circuit 3 is the pulse train shown inFIGURE 4, which lasts for a time interval equal to T The ordinate of thegraph of FIGURE 4 represents the pulse amplitude A while the abscissarepresents time f. The distance from one pulse to the adjacent pulse isshown to be equal to l/f. Similar pulse trains appear at the outputs ofgate circuits 3', 4 and 4'. The respective pulse trains are applied tocounter circuits 8, 9, 10, 11. Each counter circuit counts the number ofpulses contained in the pulse train fed into the counter circuit. Thetotal number of pulses, i.e. the counted value, represents the output ofthe counter circuit. The outputs of circuits 8 and 9 are applied to amultiplication circuit 12 and the outputs of circuits 10 and 11 to amultiplication circuit 13. Each multiplication circuit multiplies thetwo counted values applied to it, and the product of the two countedvalues represents the output of the multiplication circuit. The outputsof the multiplication circuits 12 and 13 are connected to suitableindicating means 14 and 15, respectively.

The output signals of components 1 and 2 of the systems shown in FIGURES2 and 3 correspond to the transit time sections T and T respectively.These time sections may be obtained in various ways by means of timemarker signals of which three related ones form a signal group. Eachsignal group consists of a reference signal Z and two time markersignals Z and Z which may be constituted, for example, by the risingflanks of pulses, by phase jumps, by the maxima or the passages throughzero of sinusoidal oscillations, by amplitude or frequency changes, andso on.

One way of obtaining T and T is by sending out the reference signal Zfrom a high frequency transmitter station at E in FIGURE 1, by pickingup this signal, after the same has traversed the distance e at the highfrequency station at P, which then, in the manner of a transponder,immediately sends out this signal which then again traverses thedistance e this time in the opposite direction-and is ultimatelyreceived by the station at E Furthermore, the signal sent out by thestation at P, after traversing the distance e is also received by thehigh frequency station at E FIGURE shows one embodiment of a system forcarrying out the above operation, the high frequency stations at E E andP being represented by the dashed rectangles. The reference signal Z isproduced by generator 16 of station E and sent out by a transmitter 17connected to an antenna 18. After the signal traverses the distance 2 itis received by antenna 19 of the station P. The antenna is connected toa receiver 20 whose output is connected to a modulator 21 which, inturn, is connected to a transmitter 22 having an antenna 23. The signalsent out from P, after again traversing the distance e is picked up byantenna 24 located at E this antenna being connected to receiver 25. Theoutput of receiver 25 is connected to one input of a combining circuit26, e.g., an OR-circuit, to whose other input is applied the referencesignal Z The output of circuit 26 is connected to a delay line 27 whichdelays the signal by a time interval corresponding to g/ v, where v isthe speed of signal propagation in the transmission lines mentioned inthe following. When the transmission line is a radio link then v=c.

FIGURE 6 shows the time relationship of signals appearing at the outputof delay line 27. The reference signal Z appears at instant t while thesignal Z appears at instant t Instant t follows instant t by a timeinterval T whose duration corresponds to the length of the distance ei.e.

Furthermore, the signal sent out by P will, after traversing the path ealso be picked up at E namely, by the antenna 28 connected to receiver29 (see FIGURE 5). The output of the receiver 29 at E is connected withone input of a further combining circuit 30 in E by means of atransmission line 31 having a length g (i.e., a length equal to thedistance between the stations at E and E which transmission linepropagates a signal at a speed v. The other input of circuit 30 isconnected to the output of delay line 27.

Consequently, there appears at the output of circuit 30, in addition tothe signals occurring at t and t a further signals Z at as shown inFIGURE 6. Here it is assumedfor the sake of consistency with FIGURElthat e is larger than e so that the time interval T between t and t issmaller than the time interval T In this case, then, x is deemed to havea positive value.

Accordingly, the output or indicating stage 32 to which circuit 30 isconnected will have applied to it the three signals Z Z and Z shown inFIGURE 6.

As shown in FIGURE 7, the values T and T can be obtained differently,the time relationship of the signals Z Z and Z applied to output stage32 remaining the same however, assuming, of course, that the otherparameters (g, 6 e are still the same. As is apparent from FIGURE 7, thestations E and B are connected so that both will transmit signalssimultaneously (the delay line 27 producing the same time delay as thetransmission line 31). Both signals are received by P, thenre-transmitted and ultimately received at E whereat they are processedor evaluated.

In practice, the output or indicating stage 32 need not be physicallylocated at E FIGURE 8 shows the details of the output stage 32 ofFIGURES 5 and 7. This stage comprises a separator stage 33 forseparating the signals Z Z and Z If these signals are in the form ofsquare wave pulses whose rising flanks constitute the time markers, thepulses can be distinguished from each other by making them of differentpulse widths. These different pulse widths can readily be produced, in amanner known per se, in the receivers 20 and 25. The separator stage 33has three output channels that yield the signals Z Z and Z respectively,These three signals, as well as a fourth signal represented by thepulses having a repetition frequency f and produced by pulse generator34, are then applied to a circuit 35 the details of which are shown inFIGURE 9. As is apparent from that figure, the circuit has four inputterminals for receiving the four signals, respectively. The signal Z isapplied via an AND-circuit to four flip-flops 36, 37, 33, 39, whichflip-flops are switched to the L-position before the measurement andthus produce the logic YES" information at the flip-flop outputsbelonging to those flip-flop sections marked by the symbol L in FIGURE9. The signal Z thus causes the first three of these flip-flops tochange their switching position while flip-flop 39 remains in theillustrated switching position. This enables the pulses of the pulserepetition frequency f to reach, via AND-circuits 41 and 42, a counterregister 43, whereat the pulses of the pulse repetition frequency f arecounted. The AND-circuit 42 is open inasmuch as its other input isconnected to the output of OR-circuit 44 which has a signal applied toit from the output of AND-circuit 45 and no signal from the output ofAND-circuit 46. If, then, a signal Z is received at instant t theflip-flop 37 is switched back to the illustrated position and theAND-circuit 45 no longer produces an output signal. Inasmuch as theAND-circuit 46 continues not to put out 'a signal, the AND-circuit 42will be unable to pass pulses of the pulse repetition frequency f to thecounter register 43. Instead, pulses of the pulse repetition frequency fare now applied, via

AND-circuit 47, to a counter register 48. The OR-circuit 49 herecorresponds to the OR-circuit 44 and the AND-circuit 50 to AND-circuit45.

When next a signal Z appears at instant t the flipflop 38 is returned tothe illustrated position, thereby blocking AND-circuits 50 and 47 andthus terminating 7 the counting operation in the counter register 4-8.The AND-circuit 51 then applies a signal via OR-circuit 52 for returningthe flip-flop 36 to the illustrated condition, so that a new measurementcan be made.

The outputs of registers 43 and 43 are connected to the inputs of amultiplication stage 53 whose output, in turn, is connected to anindicating stage 53a (cf. components 12 and 14 of FIGURE 2). Thealgebraic sign of x is represented by the position of the flip-flop 39.

If, however, the signal Z appears ahead of Z the flipflop 38 rather thanflip-flop 37 will first be actuated. The flip-flop 39 is then switchedinto its other position by means of a signal via AND-circuit 46. Thepulses of the pulse repetition frequency f can then pass through AND-circuit 42 as well as AND-circuit 47 so that both counter registers 43and 48 will carry out their respective counting operations. When thesignal Z then arrives at instant t the flip-flop 37 is switched, and aswitching signal is applied, via AND-circuit 51 and OR-circuit 52, toflipflop 36, which is thereby switched into the illustrated condition,thus blocking the AND-circuit 41. The other input of OR-circuit 52 isconnected to the output of a multiplication stage 53 to whose inputs thesignals Z and Z are applied.

The circuit of FIGURE 9 can be modified so that instead of countingpulses of the pulse repetition frequency f in both counter registers thecounter register 43 will count pulses of the pulse repetition frequency1, whereas the counter register 48 will count pulses of the pulserepetition frequency f in which case the single frequency generator ofFIGURE 8 will, as shown in FIGURE 19, be replaced by two generators 34'and 34". The circuit of FIGURE 9 will then be modified as shown in FIG-URE 20.

The entire system for obtaining T and T can be inverted, in a manner ofspeaking, by letting the station at the point P, whose position is to beplotted, be the one which sends out the reference time marker signal.Such a system is shown in FIGURE 16. Here, the signal sent out by P ispicked up by the station at E which, now acting as a transponder,thereupon sends out a signal which is received at both P and E Here thestation at E also acts as a transponder in that, upon receipt of thesignal from E it sends out a signal which is then received at P. In P,the transit time between E and E i.e., the distance g, is compensatedfor by delaying the signal received from E by a time intervalcorresponding to g/ v; the reference signal sent out by P is similarlydelayed. Thus, there is obtained a time relationship between the signalsZ Z and Z as shown in FIGURE 6. In FIGURE 16, the station at P is shownas being equipped with two separate receivers, namely, the receiver 25for receiving the signal from E and a second receiver 25 for receivingthe signal from E According to another embodiment of the presentinvention, the time intervals T and T are obtained as follows: The twohigh frequency stations at E and E send out, at an instant t at which areference signal Z is produced at P, time marker signals which arereceived at P at instants t and t as signals Z and Z respectively. Thisis shown in FIGURE 10, in which it is assumed that the positions ofpoints P, E; and E correspond to those shown in FIGURE 1. Basically,FIGURE is analogous to FIGURE 6.

FIGURE 11 is a block diagram of a system according to the last-mentionedembodiment. The time marker signals are produced at the transmitter sideby a generator 54 Whose output is connected to a delay line 55 whichdelays the signal by a time interval 57/ v. The output of the delay lineis connected to a transmitter 56 having an antenna 57 which sends outthe signal. Station E is connected to station E via a transmission line58 having a length g and electrical characteristics such as transmissionline 31, this line 58 serving to synchronize the time marker signalgenerator 59 at E with the time marker signal generator 5% at E Theoutput of the delay line is connected to a transmitter 60 having anantenna 61 which sends out the signal. Consequently, the signals aresent out by E and E in synchronism with each other. These signals arepicked up by the antenna 62 at P at instants t and t as signals Z and Zrespectively. Antenna 62 is connected to receiver 63. The station at Pfurther includes a reference time marker signal generator 64 whichproduces the signal Z All three signals Z Z and Z are applied to theoutput stage 65.

FIGURE 12 shows the details of the output stage 65. The signals Z and Zare separated in a separator stage 66, the same corresponding to theseparator stage 33 of FIGURE 8. The actual output circuit 67 then hasapplied to it, at separate input terminals, the three signals Z Z and Zas well as pulses of the pulse repetition frequencies f and 2 comingfrom the generators 68 and 69, respectively.

The details of circuit 67 are shown in FIGURE 13. At first, theflip-flops 7G, 71, 72, are in their switching positions as shown.Therefore, when the signal Z appears, the same is passed on by theAND-circuit 73. The flip-flop 71 is then switched into its otherswitching position and the AND-circuit 74 passes pulses of the pulserepetition frequency 2 via OR-circuit 75, to the counter register 76.When the signal Z appears at instant t the same is applied viaOR-circuit 77 and AND-circuit 78 to flip-flop 72, thereby switching thesame into its nonillustrated switching position. The AND-circuit 74 isthereby blocked and pulses of the pulse repetition frequency f areapplied via AND-circuit 79, firstly, to the counter register 8% andsecondly, via the OR-circuit to the counter register 76. The counterregister 76 thus adds to the series of pulses of pulse repetitionfrequency 2f which were fed into the counter register during the transittime interval T a further series of pulses of the repetition frequency 1during the transit time interval T So long as the flip-flop 72 remainsin the non-illustrated switching position, the AND-circuit is blockedand the flip-flop 76 remains in the illustrated switching position. Whenthere then appears the signal Z at instant t the same is applied viaOR-circuit 77, AND-circuit 82 and OR-circuit 33 to flip-flop 71, therebyswitching the latter back into its illustrated switching position. This,in turn,

causes the fiip-fiop 72 to be switched back into the illustratedswitching position.

If, however, Z arrives ahead of Z all that additionally happens is thatthe AND-circuit 31 switches the flip-flop 70 into its non-illustratedswitching position, which indicates the fact that the algebraic sign ofx is negative.

If Z and Z arrive simultaneously, they reach flipflop 71 via AND-circuit84 and OR-circuit 83, so that this flip-flop is switched back into theillustrated switching position. The register 89 thus remains empty andx=0. Also shown is a further AND-circuit 85 which switches the flip-flop76 into the illustrated switching position if Z arrives ahead of Z andinto the other switching position if Z arrives ahead of Z Instead ofusing only the pulse repetition frequency f and its harmonics, it ispossible to use the pulse repetition frequencies f 2 and f in which casethe two pulse generators 68 and 69 of FIGURE 12 will be replaced bythree pulse generators 68', 69' and 69 for producing pulses of the pulserepetition frequencies f 2f and f respectively, as shown in FIGURE 21.The circuit of FIGURE 13 will then be modified as shown in FIGURE 22.The pulses of the pulse repetition frequencies f and f are applied toAND-circuits 79 and 7?".

The arrangement last-described may also be inverted, by letting a timemarker signal be sent out by P at the instant t which signal is receivedby the stations at E and E The signal received at E is transmitted to EE produces a reference signal Z at instant t =t +g/v, and the signalreceived at E from P is delayed by g/v. The time relationship betweenthe signals will again be that shown in FIGURE 10. A system whichoperates in such a manner is shown in FIG- URE 17, wherein 16' is thereference signal generator for producing the reference signal Z, in EThe values T and T may be obtained yet another way, as follows: each ofthe stations at E and E sends out a time marker signal at the instant twhich signals, after having traversed the distances e and 2respectively, are received at P from whence they are again Sent out.Station E receives that signal from P which corresponds to the signaloriginally sent out by E while E receives from P the signalcorresponding to the signal originally sent out by E Such a system isshown in FIGURE 14. Signals are generated in E by a generator 86, and,after being delayed in delay line 87 by a time interval g/v, are sentout at instant t by means of the transmitter 88 and antenna 89. Thistransmission occurs simultaneously with the transmission of the signalfrom E which incorporates a synchronized signal generator 90, atransmitter 91 and an antenna 92. These signals are picked up at P bythe antenna 93 and receiver 94, and immediately re-transmitted bytransmitter 95 and antenna 96. The signal originally emanating from Eand retransmitted by P is then picked up by antenna 97 and receiver 99in E while the signal originally emanating from E and re-transmitted byP is picked up by antenna 98 and receiver 100 in E A delay line 101,which delays the signal by a time interval g/v, is interposed betweenthe receiver 99 and the output circuit 67 (shown in detail in FIGURE13). A similar delay line 102 is interposed between stages 87 and 67 inorder to compensate for the time it takes for the signal to travel fromreceiver 100 to the output circuit 67. Instead of pulses of the pulserepetition frequencies f and 2f, the output stage 67 has applied to itpulses of the pulse repetition frequencies f/ 2 and produced by pulsegenera-tors 103 and 104, respectively. Again assuming the relativepositions of P, E and E to be as shown in FIGURE 1, the signals Z Z Zappear as represented in FIGURE 15.

Here, too, the system can be operated, instead of solely with pulses ofthe pulse repetition frequency f and its sub-harmonics, with pulses ofthe pulse repetition frequencies f l/2f and 1/2f in which case thesystem of FIGURE 14 will be modified to include, in lieu of the pulsegenerators 103 and 104, three pulse generators 103', 104 and 104", forproducing pulses of the three pulse repetition frequencies f 1/2f and1/27 as illustrated in FIGURE 23. FIGURE 22 shows how the system ofFIGURE 13 will then be modified. The pulses of the pulse repetitionfrequencies f,, 1/27 and 1/2 are applied to AND-circuits 74, 7'9, and79", as indicated.

This third embodiment may likewise be inverted. A time marker signal issent out from P at instant t which signal is received by the stations atE and E which then, in the manner of transponders, re-transmi-t thesignals. T-hese last-mentioned signals are then picked up at P, whereinthe time relationship between the signals will be as shown in FIGURE 15.Such a system is illustrated in FIGURE 18.

Insofar as the delay of the time marker signals is concerned, it ispointed out that if the signals are received in a staggered timerelationship which is not due solely to the transit time of the signalsbetween P and the fixed points E and E these signals will, prior to orduring the measurment, have to be so delayed that the sum of all delayswhich are not due to the transit time of the signals between P and thefixed points E and E is the same for each signal.

These delays can, as described above, be produced by means of delaylines. Basically, however, it is not absolutely essential to make use ofsuch delay lines. Instead, it is in many cases expedient to simulate thedelay by letting the counting operation or operations commence not withthe value zero but with a positive or negative value which correspondsto the delay. In the arrange ments shown in FIGURES 1 and 2, in whichthe output signals of the components 1 and 2 shall represent the timeintervals T and T this would not be possible if the delays are notcompensated for by means of delay lines. For example, in the case wherethe-re is no delay compensation, the output signal of block 1 mayrepresent not the time interval T but a time interval T -l-T where Trepresents the delay not yet compensated i.e. for example TF C Thisadditional time interval T can, in this example, be easily compensatedfor by setting the counter 8 to a negative starting value equal to T f,or by setting the counter 10 to a negative starting value equal to T -fSimilarly, delay time intervals supplemental to T can be compensated forby appropriately presetting the counters '9 and 1-1.

It will be appreciated that, while the above description relates only tothe determination of the distance x between a plane F and the plane ofsymmetry F between two points E and E of known location, the position ofthe point P within the plane F can be obtained by determining thedistance between a second plane F containing the point P and a secondplane of symmetry F of two other stations E and E which plane F forms anangle, preferably a right angle, with the first plane F In practice, oneof the two points E and E may coincide with one of the points E and E orthe stations E E E E may be otherwise arranged in any suitable manner soas to form a grid or coordinate system of positional planes so that thelocation of point P may be definitely fixed, as is fully described inthe above-mentioned co-pending applications.

It will also be understood that, particularly if the measurement is tobe made at or in conjunction with one of the ground stations, the pointP need not necessarily incorporate an active transmitter. That is tosay, instead of there being a transponder at P, it may sufiice if pointP is passive, i.e., if signals transmitted from the ground stations aresimply reflected by the aircraft or the like whose position-at point Pis to be determined. Point P may thus re-transmit a signal either byacting as a transponder which actually re-broadcasts the signal, orsimply by reflecting a signal.

It will be understood that the above description of the presentinvention is susceptible to various modifications, changes, andadaptations, and the same are intended to be comprehended within themeaning and range of equivalents of the appended claims.

What is claimed is:

1. A method of determining the distance x between a plane F containing apoint P and the plane of symmetry between two high frequency stations atE and E which are spaced apart a distance g according to the equationtition frequency C f V 2 D 1 1 wherein c is the propagation velocity ofthe signals travelling said distances e and 2 and D represents anarbitrarily selectable unit of length into which g is to be substituted;

(b) counting the number of pulses of both transit time sections; and

(c) multiplying the counted values by each other; and

(-d) determining whether the transit time between one of the twostations and P is shorter or longer than the transit time between theother of the two stations and P, thereby to derive an algebraic sign forx to indicate on which side of the plane of symmetry P the plane F lies.

2. The method as defined in claim 1 wherein said factors (e -|e and Ke-2 are obtained as transit time sections T =(e -|-e )/c and T =|(e e)|/c, respectively, by transmitting a time marker signal from one of thetwo stations at an instant t re-transmitting said signal from P so thatthe same is received by the other of the two stations at an instant tand by said one station at an instant t the time difference between 1and t corresponding to the transit time section T and the timedifference between t and t corresponding to the transit time section Tand using the time marker signal and the received signal of said onestation and the received signal of said other station in their originaltime relationship t t t to mark the transit time sec-tions T and T atthe place where the measurement is to be obtained.

3. The method defined in claim 1 wherein said factors (c -H and |(e eare obtained as transit time sec tions T =(e +e )/c and T =|(e e )|/c,respectively, by transmitting a time marker signal from the one stationand from the other station at an instant t re-transmitting each of saidsignals from P so that said one station receives the signal whichoriginally emanated from said one station at an instant t and the signalwhich originally emanated from the other of said stations at an instantt the time difference between t and t corresponding to the transit timesection T and the time difference between t and t corresponding to thetransit time section T and using the time marker signal of one of thetwo stations and the signals which the one station receives from saidone station via P and from said other station via P in their originaltime relationship t t t to mark the transit time sections T and T at theplace at which the measurement is to be obtained.

4. The method defined in claim 1 wherein said factors (e +e and |(e eare obtained as transit time sections T :(e -|-e )/c and T =|(e e )|/c,respectively, by producing a reference signal and simultaneouslytransmitting a marker signal from P; re-transmitting said marker signalfrom one of the stations; receiving the retransmitted marker signal fromsaid one station at P as well as at the other of the stations; delayingthe reference signal as well as the signal received at P by a timeinterval corresponding to the transit time between the two stations sothat the signals appear at instants t and t respectively;re-transmitting from said other station the signal received from saidone station; receiving the last-mentioned retransmitted signal at P atthe instant t the time difference between 2; and t corresponding to thetransit time section T and the time diiference between t and 1corresponding to the transit time section T and using the delayedreference signal and the delayed signal which P received from the onestation and the undelayed signal which P received from the other stationin their original time relationship t t 1 to mark the transit timesections T and T at the place at which the measurement is to beobtained.

5. The method defined in claim 1 wherein said factors (c l-e and [(e eare obtained as transit time sections T =(e +e )/c and T =[(e -e )[/c,respectively, said section T being transformed into a pulse traincontaining pulses of a pulse repetition frequency f, and said section Tbeing transformed into a pulse train containing pulses of a pulserepetition frequency f wherein 6. The method defined in claim 1 whereinsaid factors (e -|-e and |(e e are obtained as transit time sections T=(e +e )/c and T =|(e e )|/c, respectively, by producing a referencesignal at the place at which the measurement is to be obtained and bysynchronously transmitting a time marker signal from each of the twostations at an instant t at point P receiving and identifying, at aninstant t after a time interval T =t t the signal transmitted by one ofthe stations and, at an instant t after a time interval T =t t thesignal transmitted by the other of the stations, where T =e /c, T =e /c,and T =|t t |:](e e )l/c, and producing, at the place at which themeasurement is to be obtained, numerical values T -f and T -fcorresponding to T =ZT +T and T T12.

7. The method defined in claim 1 wherein the factors '(e -l-e and |(e e)l are obtained as transit time sections T =(e +e )/c and T =|(e e )|/c,respectively, by producing, at an instant t a reference signal at one ofthe two stations and, at the same instant t transmitting a time markersignal from P; receiving the transmitted time marker signal at said onestation; delaying the reference signal and the received time markersignal in said one station by a time interval corresponding to thetransit time between the two stations so that the signals appear at tand t respectively; receiving at the other of the stations the timemarker signal transmitted by P; re-transmitting from said other stationthe signal received from P; receiving the last-mentioned re-transmittedsignal at said one station at [2, T1 f1t0, T2=[2t and T g if tgi; andproducing, at the place at which the measurement is to be obtained,numerical values T and T -f corresponding to T =2T +T and T =T 8. Amethod as defined in claim 6 wherein the value T -f is represented by afirst value; wherein the value T -f is represented by the sum of thefirst value and a second value; wherein the first value is obtained asthe number of pulses of the pulse repetition frequency f counted duringthe time interval T wherein the second value is obtained as the numberof pulses of the pulse repetition frequency 2] counted during the timeinterval T wherein the value T -f is obtained by adding the first andthe second value.

9. A method as defined in claim 7 wherein the value T 'f is representedby a first value; wherein the value T -f is represented by the sum ofthe first value and a second value; wherein the first value is obtainedas the number of pulses of the pulse repetition frequency 1 countedduring the time interval T wherein the second value is obtained as thenumber of pulses of the pulse repetition frequency 2 counted during thetime interval T wherein the value T -f is obtained by adding the firstand the second value.

It). A method as defined in claim 1 wherein the factors (e +e and |(e eare obtained as transit time sections T =(e +e )/c and T =|(e -e )[/c,respectively, by producing a reference signal at t at the place at whichthe measurement is to be made; by simultaneously transmitting a timemarker signal from each of the two stations at t receiving andre-transmitting each of the two time marker signals at P; receiving thatre-transmitted time marker signal at the one station at t whichrepresents the reply signal for the time marker signal transmitted bythe one station; receiving that re-transmitted time marker signal at theother station at t which represents the reply signal for the time markersignal transmitted by the other station; applying the reply signals tothe place at which the measurement is to be made to obtain thereat, incombination with a reference signal,

markings of the three instants t t and t where the time intervalscorrespond solely to the transit times of signals and to transit timedifferences between P and the two stations; and producing numericalvalues T -f and T f corresponding to the sections T =T +T /2 and T =T/2, respectively.

11. A method as defined in claim 1 wherein the factors (e +e and [(e eare obtained as transit time sections T =(e +e )/c and T =|(e e )[/c,respectively, by producing a reference signal at t at the place at whichthe measurement is to be made; by transmitting a time marker signal fromP at t by receiving said transmitted signal from P at the two stationsand re-transmitting said received signals from the two stations; byreceiving at t the re-transmitted signal from one of the two stations atP, by receiving at t the re-transmitted signal from the other of the twostations at P, with T =t t T =t -t and T =]t t and producing, at theplace at which the measurement is to be obtained, numerical values T -fand T,,-] corresponding to T =T +T /2 and T =T /2.

12. A method as defined in claim wherein the value T -f is representedby a first value; wherein the value T is represented by the sum of thefirst value and a second value; wherein the first value is obtained asthe number of pulses of the pulse repetition frequency f/Z countedduring the time interval T wherein the second value is obtained as thenumber of pulses of the pulse repetition frequency f counted during thetime interval T wherein the value T f is obtained by adding the firstand the second value.

13. A method as defined in claim 1 wherein the frequency f is soselected that the numerical value of is an integral power of ten.

14. A method as defined in claim 6 wherein, during the time interval Tpulses of the pulse repetition frequency Zf are counted; wherein, duringthe time interval T pulses of the pulse repetition frequencies f and fare counted separately; wherein there is formed the sum of the numericalvalues of the pulses of the pulse repetition frequencies f and Zfcounted during the time intervals T and T respectively, for determininga numerical value T f =T -2 +T -f corresponding to the section T andwherein there is evaluated the value representing the number of pulsesof the pulse repetition frequency f counted during the time interval Tfor determining a numerical value T -f =T -f corresponding to thesection T with 15. A method as defined in claim 7 wherein, during thetime interval T pulses of the pulse repetition frequency Zf are counted;wherein, during the time interval T pulses of the pulse repetitionfrequencies f and f are counted separately; wherein there is formed thesum of the numerical values of the pulses of the pulse repetitionfrequencies f and Zf counted during the time intervals T and Trespectively, for determining a numerical value T -f =T -2 +T -fcorresponding to the sec tion T and wherein there is valuated the valuerepresenting the number of pulses of the pulse repetition frequency fcounted during the time interval T for determining a numerical value T f=T f corresponding to the section T with c2 2.f D 16. A method asdefined in claim 10 wherein, during the time interval T pulses of thepulse repetition frequency f are counted; wherein during the timeinterval T pulses of the pulse repetition frequencies f /2 and f 2 arecounted separately; wherein there is formed the sum of the numericalvalues of the pulses of the pulse repetition frequencies f and f /Zcounted during the time intervals T and T respectively, for determininga numerical value T -f corresponding to the time section T :1 +T 2; andwherein there is evaluated the value representing the number of pulsesof the pulse repetition frequency f /Z counted during the time intervalT for determining a numerical value T -f =T -f /2 corresponding to thesection T with 2 v f8 D 17. A method as defined in claim 11 wherein,during the time interval T pulses of the pulse repetition frequency fare counted; wherein during the time interval T pulses of the pulserepetition frequencies f /Z and f /Z are counted separately; whereinthere is formed the sum of the numerical values of the pulses of thepulse repetiti-on frequencies i and f 2 counted during the time intervals T and T respectively, for determining a numerical value L;corresponding to the time section and wherein there is evaluated thevalue representing the number of pulses of the pulse repetitionfrequency f 2 counted during the time interval T for determining anumerical value T -f zT -f /2 corresponding to the section T with 2 f8-2. .D 18. A method as defined in claim 5 wherein the frequencies i and fare so selected that the numerical value of I is an integral power often.

19. A method as defined in claim 1 wherein C2 'fP- where n represents aconversion factor for converting the distance g into the desired unit oflength of x, B being equal to k-D where k is an arbitrarily selectableconstant.

20. A method as defined in claim 5 wherein -L 2.u .f .f .g where urepresents a conversion factor for converting the distance g into thedesired unit of length of x, D being equal to k-D where k is anarbitrarily selectable constant. 21. A method as defined in claim 1wherein, in the event the signals are received, at the place where themeasurement is to be made with different time delays, where said timedelays are not caused by the transmission paths between each of the twostations and P, the counting operation or operations commence with avalue or values other than zero, which other values or values algebraicsign and magnitude are so selected that the error or errors which suchdifferent time delays would introduce in the value or values obtainedfrom the counting operation or operations is or are compensated for.

22. A system for determining the distance at between a .plane Fcontaining a point P and the plane of symmetry F between two highfrequency stations at points

1. A METHOD OF DETERMINING THE DISTANCE X BETWEEN A PLANE FP CONTAININGA POINT P AND THE PLANE OF SYMMETRY BETWEEN TWO HIGH FREQUENCY STATIONSAT E1 AND E2 WHICH ARE SPACED APART A DISTANCE G ACCORDING TO THEEQUATION